ELECTRICITY AND MAGNETISM. 107 



Force dua to a Magnetic Shell. A mag- 

 netic shell (Art. -n exerts a magnetic force upon a mag- 

 net pole placed at a point in its neighbourhood. If the 

 shell be flat and very great, as compared with the distance 

 of the point considered, this force will be independent of 

 that distance, will be normal to the shell in direction, and 

 will depend only upon the amount of magnetism on the 

 shell, and will be numerically equal to 2?r times the 

 quantity of magnetism per square centimetre 1 (i.e. to 

 2T<r when <r is the " surface density " of magnetism on 

 the face of the shell). 



If the shell is bounded, however, by a limiting area, 

 the force exerted by a shell upon a point outside it will 

 be greater near to the shell than at a distance away. 

 In this case it is most convenient to measure not the 

 force but the potential due to the shell. The defini- 

 tion of " magnetic potential " is given in Art. 310 ; mean- 

 time we may content ourselves with stating that the 

 potential due to a magnetic shell at a point near it, is 

 equal to the strength of the shell multiplied by the solid 

 angle , 2 subtended by the shell at that point. 



128. A Magnetic Paradox. If the N.-seeking 

 pole of a strong magnet be held at some distance from 

 the N.-seeking pole of a weak magnet, it will repel it ; 

 but if it is pushed up quite close it will be found now to 

 attract it. This paradoxical experiment is explained 

 by the fact that the magnetism induced in the weak 

 magnet by the powerful one will be of the opposite kind, 

 and will be attracted ; and, when the powerful magnet is 

 near, this induced magnetism may overpower and mask 

 the original magnetism of the weak magnet. The 

 student must be cautioned that in most of the experi- 

 ments on magnet poles similar perturbing causes are at 

 work. The magnetism in a magnet is not quite fixed, 



1 The proof of this proposition is similar to that given at end of Lesson 

 XX., for the analogous proposition concerning the force due to a flat plate 

 charged with electricity. 



2 See Note on " Ways of Reckoning Angles," at the end of this Lesson. 



